Abstract
For the first time, the production of a massive dark photon (DP) in the \(\gamma e^-\) scattering at the future lepton colliders ILC, CLIC, and CEPC is examined. The invisible decay mode of the DP is addressed. We have studied both the unpolarized scattering and the collision of the Compton backscattered photons with the polarized electron. The missing energy distributions are shown. We have considered the wide range 1–1000 GeV of the DP mass \(m_{A'}\). The excluded regions at the 95% CL in the plane \((\varepsilon , m_{A'})\), where \(\varepsilon \) is the kinetic mixing parameter, are obtained. In particular, in the low mass region, 1–10 GeV our bounds for the 90 GeV CEPC are several times stronger than experimental limits obtained by the BaBar collaboration. For the polarized scattering, the excluded bounds for all three colliders are approximately 20% stronger as compared with the unpolarized case.
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1 Introduction
One of the main goals of the present and proposed collider experiments is to search for dark matter (DM) particles. The DM makes up approximately 85% of the total mass in the Universe. Its existence is firmly confirmed by gravitational experiments [1, 2], but composition and nature are still an open question. We consider a DM scenario in which no DM fields are charged under the SM gauge group, and the lightest stable DM particles, \(\chi \), can only interact with SM through the exchange of a vector mediator, dark photon (DP) (also known as hidden or heavy photon) [3,4,5,6,7,8,9,10,11,12]. It is usually denoted as \(A'\). In its turn, the DP kinetically mixes with the SM \(U(1)_Y\) hypercharge gauge field at the renormalizable level (kinematic-mixing portal) [7]. Such mixing can be generated by loops of massive particles charged under both \(U(1)_Y\) and secluded \(U(1)'\) symmetries. That kinetic-mixing portal model may be extended to 5D by adding one flat ED [13]. The existence of a new light dark sector can be also connected to a generation of neutrino masses [14]. An electroweak gauge extension of the SM by adding an extra \(U(1)'\), with mixing with the standard \(U(1)_Y\) can also result in a new boson [15,16,17]. For recent reviews on the DP, see, for instance, [18,19,20,21,22,23,24,25]. In particular, astrophysical constraints on the DP parameters can be found in [26,27,28,29,30,31,32,33,34], while bounds from \((g-2)_{\mu ,e}\) are presented in [35, 36].
The main mechanisms of the DP production are meson decays (\(\pi ^0, \eta \rightarrow A' \gamma \)) [37], bremsstrahlung (\(eZ \rightarrow eZA'\) and \(pZ \rightarrow pZA'\)) [38, 39], Drell-Yan (\(q {\bar{q}} \rightarrow A'\)), and annihilation (\(e^+e^- \rightarrow A' \gamma \)). The process of pair annihilation into a dark and an ordinary photon provided a striking benchmark (mono-photon plus missing energy) for the DP search at the LEP [40,41,42,43]. A probing new physics in final states containing a photon and missing transverse momentum in proton-proton collisions was presented by the ATLAS and CMS Collaborations [44,45,46,47]. For the most recent results on the DPs from the LHC, see [48,49,50,51]. The ATLAS and CMS search sensitivities for DPs at the high luminosity LHC can be found in [52, 53]. A DP phenomenology at the LHC and HL-LHC was studied in [54,55,56,57], and searches of the DPs at the LHeC and FCC-he colliders were discussed in [58].
A probing new light gauge boson similar to the photon in \(e^+e^-\) collisions is of particular interest [59,60,61,62,63,64,65,66,67,68,69,70,71,72]. The searches for the DP at \(e^+e^-\) colliders [73,74,75,76,77,78] (see also review papers [18,19,20,21,22,23,24,25]) have looked for its decays to the \(e^+e^-, \mu ^+\mu ^-\) and \(\pi ^+\pi ^-\) final states, as well as for invisible decays of \(A'\). The DP production in the Compton-like \(\gamma e \rightarrow A' e\) process is studied in [79, 80]. The inverse process, \(A' e \rightarrow \gamma e\), is recently considered in [81]. The gamma factory’s discovery potential through the low energy dark Compton scattering is analyzed in [82]. In [83] the \(\gamma \gamma \rightarrow \gamma A'\) process for MeV scale collider is considered.
In the present paper we examine a novel DP production based on a high energy \(\gamma e^-\) scattering at the lepton colliders ILC [84, 85], CLIC [86, 87], and CEPC [88, 89], the \(\gamma e^- \rightarrow A' e^-\) process. Both unpolarized and polarized collisions are considered in the wide DP mass region 1–1000 GeV. We expect the DP to decay predominantly into invisible dark-sector particles. Let us underline that up to now the DP production at high energy lepton colliders was studied only for the \(e^+e^-\) mode of these colliders [68,69,70,71].
2 Massive dark photon
As it was already mentioned above, the DP does not directly couple to SM fields. But there could be a small coupling to the electromagnetic current \(J_\mu \) due to kinetic mixing between the SM hypercharge and the field strength tensor of the DP field. Consider the case when the dark sector is represented by just a single extra \(U(1)'\) gauge group. Let \(B_\mu \), \({\bar{A}}'_\mu \) be the mediator fields of the SM \(U(1)_Y\) symmetry and dark \(U(1)'\) gauge group. The gauge Lagrangian can be taken in the following form
where \(B_{\mu \nu } = \partial _\mu B_\nu - \partial _\nu B_\mu \) and \({\bar{F}}'_{\mu \nu } = \partial _\mu {\bar{A}}'_\nu - \partial _\nu {\bar{A}}'_\mu \) are the field strength tensors of \(U(1)_Y\) and \(U(1)'\), respectively, \(c_W\) is the cosine of the Weinberg angle \(\theta _W\), and \(\varepsilon \ll 1\) is the kinetic mixing parameter. The kinetic mixing can be generated at the one-loop level by massive particles charged under both \(U(1)_Y\) and \(U(1)'\) symmetries. After diagonalization of the gauge fields \(W^3_\mu \), \(B_\mu \), and DP field \({\bar{A}}'_\mu \) [23],
where \(s_W\) and \(t_W\) are the sine and tangent of \(\theta _W\), we obtain the interaction Lagrangian up to \(\mathrm {O}(\varepsilon ^2)\)
Here \(A_\mu \), \(Z_\mu \) are the physical gauge fields, and \(A'^\mu \) is the physical field of the DP. \(J'_\mu \) and \(e'\) are the DM matter current and DP coupling to the dark-sector matter, respectively. In (3) we have added the last term which describes a \(A'\chi \chi \) interaction, where \(\chi \) is a dark matter particle. The form of this interaction is left unspecified. As one can see in (3), the coupling of the massive DP the SM fermions is \(-\varepsilon e\). The Z gauge boson acquires the coupling strength \(\varepsilon e' t_W\) to the dark sector current.
Thus, there are three unknown parameters: the DP mass, \(m_{A'}\), the mixing parameter, \(\varepsilon \), and the \(A'\rightarrow \chi {\bar{\chi }}\) branching. The latter is taken to be unity, if we assume that \(m_{A'} > 2m_\chi \). The dimensionless mixing parameter \(\varepsilon \) is a priori unknown and presumably lies in the \(10^{-12} - 10^{-2}\) region, depending on the DP mass [33, 39, 90,91,92,93,94,95] (see also Fig. 8.16 in [96], where sensitivities for the DP in the plane mixing parameter \(\varepsilon \) versus \(m_{A'}\) are collected). The DP mass \(m_{A'}\) can also vary in a wide range, but most of experimental searches for the invisible DP were aimed at the \(m_{A'}\) in the region \(1 \mathrm {\ MeV} - 10 \mathrm {\ GeV}\) [18,19,20,21,22,23,24,25], see Fig. 1. We will examine the wider DP mass region 1–1000 GeV.
3 Invisible dark photon production in Compton-like scattering
The production of the DP in the center-of-mass system of the \(\gamma e^-\) scattering,
is depicted in Fig. 2. As is known, linear \(e^+e^-\) colliders can operate in \(\gamma e\) and \(\gamma \gamma \) modes [97,98,99]. The \(\gamma \gamma \) facilities at the future circular colliders are examined in [100,101,102,103,104]. In particular, a number of processes in \(\gamma e\) and \(\gamma \gamma \) collisions at the CEPC have been studied in [105]. At the lepton collider hard real photons may be generated by the laser Compton backscattering, when soft laser photons collide with electron beams. As a result, a large flux of photons is produced which carry a great amount of the parent electron energy. A \(\gamma e\) (\(\gamma \gamma \)) collider has a number of advantages over \(e^+e^-\) collider. Among they are (i) Higgs can be s-channel produced; (ii) higher cross sections for charged particles; (iii) higher mass reach in some channels; (iv) pure QED interaction (in \(e^+e^-\) a Z boson exchange is present); (v) higher polarization of initial states. The \(\gamma e\) and \(\gamma \gamma \) modes were considered for a number of processes at the future lepton colliders [106,107,108,109,110,111,112,113,114,115,116,117], but the DP production in \(\gamma e\) or \(\gamma \gamma \) collisions have not yet been studied at the ILC, CLIC, or CEPC.
Let \(E_0\) be the energy of the initial laser photon beam, \(E_e\) be the energy of the initial electron beam, while \(E_\gamma \) be the energy of the Compton backscattered (CB) photon. The differential cross section for the unpolarized DP production accompanied by electron at the lepton collider operating in the \(\gamma e\) mode is defined as
Here \(f_{\gamma /e}(x)\) is the distribution of the CB photon in the variable \(x = E_\gamma /E_e\),
\(p_\bot \) is the transverse momentum of the outgoing particles, m is the electron mass, and \(\theta \) represents the scattering angle of the outgoing DP (see Fig. 2). The laser beam energy \(E_0\) is chosen to maximize \(E_\gamma \). It is achieved, if \(\zeta = 4.8\), and we get \(x_{\max } = 0.83\), see Eq. (6).
The spectrum of the CB photons in formula (5) is defined as follows [97]
where
The differential cross section for the process \(\gamma e^- \rightarrow A' e^-\) in the center-of-mass system of the colliding particles is defined as
where \(\sqrt{{\hat{s}}} = \sqrt{sx}\) is the center-of-mass energy of the backscattered photon and electron, \({\hat{s}} \geqslant (m_{A'} + m)^2\). A matrix element of the process (4) is a sum of two diagrams in Fig. 3, in which the \(A'e^-e^+\) coupling constant is equal to \(-\varepsilon e\). An explicit expression for the square matrix element \(|F|^2\) is given in Appendix A.
The main background comes from the SM process
see the diagrams in Figs. 4 and 5. In detector it looks like an event with an isolated electron and missing transverse energy. We apply the cut on the transverse momenta of the final electron, \(p_\perp > 10\) GeV, and its rapidity, \(|\eta | < 2.5\). In order to reduce the SM background, we also impose the cut on an invisible invariant mass, \(|m_{A'} - m_{\mathrm {invis}}| < 5\) GeV. In numerical calculations, especially in background calculations, CalcHEP program was also used [118]. We have used the following statistical significance (SS) formula [119],
where S and B are the numbers of the signal and background events, respectively. Note that \(SS \simeq S/\sqrt{B}\) for \(S \ll B\).
In Figs. 6, 7 and 8 we present differential cross sections of the \(\gamma e^- \rightarrow e^- + E{\!\!\!\!/}\) scattering as functions of the missing energy for a fixed value of the mixing parameter \(\varepsilon \). The results for the colliders CEPC, ILC, and CLIC are given, for the DP masses \(m_{A'} = 50\) GeV, 100 GeV, and 200 GeV, respectively. In all figures, red (black) curves correspond to the cross sections with (without) account of the dark photon contributions. It turns out that DP is the dominant effect for high missing energy values. We have also made calculations for different values of \(m_{A'}\). Our calculations show that deviations of the cross sections from the SM predictions become smaller as the DP mass \(m_{A'}\) grows.
The excluded bounds for the massive DP going to invisible final states are presented in Figs. 9 and 10 in the plane the kinetic mixing parameter \(\varepsilon \) versus DP mass \(m_{A'}\). In Fig. 9 the results for the unpolarized \(\gamma e^- \rightarrow A' e^-\) collision are given for the CEPC (left panel), ILC (middle panel), and CLIC (right panel). The strongest bound on \(\varepsilon \) is achieved for the 90 GeV CEPC. In the region \(m_{A'} = 1\)–10 GeV it is 2–4 orders of magnitude stronger than the experimental bounds obtained by the BaBar collaboration shown in Fig. 1. The constraints for the ILC collider with the energy of 160 GeV and 240 GeV are comparable with the BaBar constraints in this mass region. The sensitivity decreases as \(m_{A'}\) grows.
The results for the polarized case are shown in Fig. 10. The polarized electron sources of the future linear colliders have been discussed in the current ILC [85], CLIC [86], and CEPC [88] designs. We consider the unpolarized CB photons and \(\mathrm {P}(e^-) = 80\%\) polarization of the initial electron beam for all three colliders. By analogy with the ILC project, we assume that for the polarized \(\gamma e^-\) collision, the CEPC integrated luminosity is 50% less than the integrated luminosity for the unpolarized \(\gamma e^-\) scattering. One can see that the obtained excluded bounds are on average 20% better compared to the unpolarized bounds (Fig. 9). For the CLIC, a 10% improvement takes place only for the energy \(\sqrt{s} = 380\) GeV. As for the electron beam polarization of \(\mathrm {P}(e^-) = -80\%\), our calculations show that it does not offer any advantage over the unpolarized case. The reason is that the SM background gets larger for \(\mathrm {P}(e^-) = -80\%\) with respect to the unpolarized collision, while the signal remains almost the same.
4 Conclusions
In the present paper, we have studied the production of the massive dark photon (DP) in the \(\gamma e^-\) scattering at the future lepton colliders ILC, CLIC, and CEPC, when the DP decays predominantly into invisible dark matter particles. The real photons are generated by the laser Compton backscattering when the soft laser photons collide with the electron beams. Both the unpolarized and polarized collisions are studied. For the polarized \(\gamma e^- \rightarrow A' e^-\) process we have assumed that the incoming CB photon is unpolarized, while the polarization of the electron beam is taken to be 80% for all three colliders. The wide region 1–1000 GeV of the DP mass \(m_{A'}\) is considered. The missing energy distributions for signal and background are presented. We have derived the excluded regions at the 95% CL in the plane \((\varepsilon , m_{A'})\), where \(\varepsilon \) is the kinetic mixing parameter. Our excluded bounds for the polarized collisions at the ILC and CEPC are approximately 20% stronger compared to the unpolarized excluded bounds. In particular, in the low mass region 1–10 GeV our excluded bounds for the 90 GeV CEPC are in average 2–4 orders of magnitude stronger that the experimental bounds obtained by the BaBar collaboration. The CEPC constraints with energies of 160 GeV and 240 GeV are comparable with the BaBar bounds in this mass range, and the ILC excluded bounds are close to them.
Note that up to now the production of the DP at future lepton colliders (both for the visible and invisible DP decays) was studied only for the \(e^+e^-\) mode of these colliders.
As was already mentioned in Introduction, the DP production in the Compton-like \(\gamma e \rightarrow A' e\) process was studied in the fixed target experiments [79, 80, 82]. However, these low energy experiments were dealing with low mass DPs (\(m_{A'} < 100\) MeV), while we examine heavy DPs (\(m_{A'} > 1\) GeV).
Our method can be also applied to dark axionlike pseudoscalars (scalars). Consider the coupling of a pseudoscalar ALP a to a electron field \(\psi \). It is given by the Lagrangian (see, for instance, [120])
Then the amplitude of the process \(\gamma e^- \rightarrow a e^-\) will be proportional to the electron mass \(m_e\). So, we expect that the pseudoscalar cross section will be suppressed with respect to the dark photon cross section. Nevertheless, we consider studying axionlike (pseudo)scalars as a future direction.
Data Availability
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: We give predictions for future colliders.]
References
V. Trimble, Existence and nature of dark matter in the Universe. Annu. Rev. Astron. Astrophys. 25, 425 (1987)
G. Bertone, D. Hooper, History of dark matter. Rev. Mod. Phys. 90, 045002 (2018). arXiv:1605.04909
P. Fayet, Effects of the spin 1 partner of the goldstino (gravitino) on neutral current phenomenology. Phys. Lett. B 95, 285 (1980)
P. Fayet, On the search for a new spin 1 boson. Nucl. Phys. B 187, 184 (1981)
L.B. Okun, Limits of electrodynamics: paraphotons? Sov. Phys. JETP 56, 502 (1982) (Zh. Eksp. Teor. Fiz. 83, 892 (1982))
P. Galison, A. Manohar, Two Z’s or not two Z’s? Phys. Lett. B 136, 279 (1984)
B. Holdom, Two \(U(1)\)’s and \(\varepsilon \) charge shifts. Phys. Lett. B 166, 196 (1986)
B. Holdom, Searching for \(\varepsilon \) charges and a new \(U(1)\). Phys. Lett. B 178, 6 (1986)
K.R. Dienes, C.F. Kolda, J. March-Russell, Kinetic mixing and the supersymmetric gauge hierarchy. Nucl. Phys. B 492, 104 (1997). arXiv:hep-ph/9610479
N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer, N. Weiner, A theory of dark matter. Phys. Rev. D 79, 015014 (2009). arXiv:0810.0713
M. Pospelov, A. Ritz, M.B. Voloshin, Secluded WIMP dark matter. Phys. Lett. B 662, 53 (2008). arXiv:0711.4866
D. Hooper, N. Weiner, W. Xue, Dark forces and light dark matter. Phys. Rev. D 86, 056009 (2012). arXiv:1206.2929
T.G. Rizzo, Kinetic mixing, dark photons and an extra dimension. Part I, JHEP 07, 118 (2018). arXiv:1801.08525
E. Bertuzzo, S. Jana, P.A. Machado, R.Z. Funchal, Neutrino masses and mixings dynamically generated by a light dark sector. Phys. Lett. B 791, 210 (2019). arXiv:1808.02500
F. Del Aguila, The physics of \(Z^{\prime }\) bosons. Acta Phys. Pol. B 25, 1317 (1994). arXiv:hep-ph/9404323
K.S. Babu, C.F. Kolda, J. March-Russell, Leptophobic \(U(1)^{\prime }\)s and the \(R_b\)-\(R_c\) crisis. Phys. Rev. D 54, 4635 (1996). arXiv:hep-ph/9603212
T.G. Rizzo, Gauge kinetic mixing and leptophobic \(Z^{\prime }\) in \(E_6\) and \(SO\)(10). Phys. Rev. D 59, 015020 (1998)
M. Raggi, V. Kozhuharov, Results and perspectives in dark photon physics. Riv. Nuovo Cim. 38, 449 (2015)
F. Curciarello, Review on dark photon. EPJ Web Conf. 118, 01008 (2016)
M. Battaglieri et al., US cosmic visions: new ideas in dark matter 2017: Community report. arXiv:1707.04591
P. Ilten, Y. Soreq, M. Williams, W. Xue, Serendipity in dark photon searches. JHEP 06, 004 (2018). arXiv:1801.04847
J. Beacham et al., Physics beyond colliders at CERN: beyond the Standard Model working group report. J. Phys. G Nucl. Part. Phys. 47, 010501 (2020). arXiv:1901.09966
M. Fabbrichesi, E. Gabrielli, G. Lanfranchi, The physics of the dark photon: a primer, SpringerBriefs in Physics (2020). arXiv:2005.01515
A. Filippi, M. De Napoli, Searching in the dark: the hunt for the dark photon. Rev. Phys. 5, 100042 (2020). arXiv:2006.04640
M. Graham, C. Hearty, M. Williams, Searches for dark photons at accelerators. Annu. Rev. Nucl. Part. Sci. 71, 37 (2021)
E.D. Carlson, Limits on a new \(U(1)\) coupling. Nucl. Phys. B 286, 378 (1987)
D.A. Dobrescu, Massless gauge bosons other than the photon. Phys. Rev. Lett. 94, 151802 (2005). arXiv:hep-ph/0411004
M. Pospelov, A. Ritz, Astrophysical signatures of secluded dark matter. Phys. Lett. B 671, 391 (2009). arXiv:0810.1502
H.K. Dreiner, J.-F. Fortin, C. Hanhart, L. Ubaldi, Supernova constraints on MeV dark sectors from \(e^+e^-\) annihilations. Phys. Rev. D 89, 105015 (2014). arXiv:1310.3826
K.-Y. Choia, K. Kadota, I. Park, Constraining dark photon model with dark matter from CMB spectral distortions. Phys. Lett. B 771, 162 (2017). arXiv:1701.01221
M. Dutra et al., MeV dark matter complementarity and the dark photon portal. JCAP 03, 037 (2018). arXiv:1801.05447
J.H. Chang, R. Essig, S.D. McDermott, Revisiting Supernova 1987A constraints on dark photons. JHEP 01, 107 (2017). arXiv:1611.03864
J.H. Chang, R. Essiga, S.D. McDermott, Supernova 1987A constraints on sub-GeV dark sectors, millicharged particles, the QCD axion, and an axion-like particle. JHEP 09, 051 (2018). arXiv:1803.00993
X. Bi et al., Axion and dark photon limits from Crab Nebula high-energy gamma rays. Phys. Rev. D 103, 043018 (2021). arXiv:2002.01796
G.W. Bennett et al., (Muon g-2 Collaboration), Final report of the muon E821 anomalous magnetic moment measurement at BNL. Phys. Rev. D 73, 072003 (2006). arXiv:hep-ex/0602035
M. Pospelov, Secluded \(U\)(1) below the weak scale. Phys. Rev. D 80, 095002 (2009). arXiv:0811.1030
P. Ilten, J. Thaler, M. Williams, W. Xue, Dark photons from charm mesons at LHCb. Phys. Rev. D 92, 115017 (2015). arXiv:1509.06765
S. Gninenko, D. Kirpichnikov, M. Kirsanov, N. Krasnikov, The exact tree-level calculation of the dark photon production in high-energy electron scattering at the CERN SPS. Phys. Lett. B 782, 406 (2018). arXiv:1712.05706
J.D. Bjorken, R. Essig, P. Schuster, N. Toro, New fixed-target experiments to search for dark gauge forces. Phys. Rev. D 80, 075018 (2009). arXiv:0906.0580
G. Abbiendi et al., (OPAL Collaboration), Search for anomalous photonic events with missing energy in \(e^+e^-\) collisions at \(\sqrt{s} = \) 130 GeV, 136 GeV and 183 GeV. Eur. Phys. J. C 8, 23 (1999). arXiv:hep-ex/9810021
M. Acciarri et al., (L3 Collaboration), Single and multiphoton events with missing energy in \(e^+e^-\) collisions at \(\sqrt{s} = \) 189 GeV. Phys. Lett. B 470, 268 (1999). arXiv:hep-ex/9910009
A. Heister et al., (ALEPH Collaboration), Single photon and multiphoton production in \(e^+e^-\) collisions at \(\sqrt{s}\) up to 209 GeV. Eur. Phys. J. C 28, 1 (2003)
J. Abdallah et al., (DELPHI Collaboration), Photon events with missing energy in \(e^+e^-\) collisions at \(\sqrt{s} = \) 130 to 209 GeV. Eur. Phys. J. C 38, 395 (2005). arXiv:hep-ex/0406019
G. Aaad et al., (ATLAS Collaboration), Search for long-lived neutral particles decaying into lepton jets in proton-proton collisions at \(\sqrt{s} = \) 8 TeV with the ATLAS detector. JHEP 11, 088 (2014). arXiv:1409.0746
M. Aaboud et al., (ATLAS Collaboration), Search for new phenomena in events with a photon and missing transverse momentum in pp collisions at \(\sqrt{s} = \) 13 TeV with the ATLAS detector. JHEP 06, 059 (2016). arXiv:1604.01306
V. Khachatryan et al., (CMS Collaboration), A search for pair production of new light bosons decaying into muons. Phys. Lett. B 752, 146 (2016). arXiv:1506.00424
A.M. Sirunyan et al., (CMS Collaboration), Search for new physics in final states with a single photon and missing transverse momentum in proton-proton collisions at \(\sqrt{s} = \) 13 TeV. JHEP 02, 074 (2019). arXiv:1810.00196
G. Aad et al., (ATLAS Collaboration), Search for new phenomena in events with an energetic jet and missing transverse momentum in \(pp\) collisions at \(\sqrt{s} = 13\) TeV with the ATLAS detector. Phys. Rev. D 103, 112006 (2021). arXiv:2102.10874
G. Aad et al. (ATLAS Collaboration), Observation of electroweak production of two jets in association with an isolated photon and missing transverse momentum, and search for a Higgs boson decaying into invisible particles at 13 TeV with the ATLAS detector. arXiv:2109.00925
A.M. Sirunyan et al., (CMS Collaboration), Search for dark matter produced in association with a leptonically decaying Z boson in proton–proton collisions at \(\sqrt{s} = \) 13 TeV. Eur. Phys. J. C 81, 13 (2021). arXiv:2008.04735
A.M. Sirunyan et al., (CMS Collaboration), Search for dark photons in Higgs boson production via vector boson fusion in proton–proton collisions at \(\sqrt{s} = \) 13 TeV. JHEP 03, 011 (2021). arXiv:2009.14009
ATLAS Collaboration, Search prospects for dark-photons decaying to displaced collimated jets of muons at HL-LHC, ATL-PHYS-PUB-2019-002 (2019)
CMS Collaboration, Search sensitivity for dark photons decaying to displaced muons with CMS at the high-luminosity LHC, CMS-PAS-FTR-18-002 (2018)
D. Curtin, R. Essig, S. Goric, J. Shelton, Illuminating dark photons with high-energy colliders. JHEP 02, 157 (2015). arXiv:1412.0018
E. Gabrielli, M. Heikinheimo, B. Mele, M. Raidal, Dark photons and resonant monophoton signatures in Higgs boson decays at the LHC. Phys. Rev. D 90, 055032 (2014). arXiv:1405.5196
A. Berlin, F. Kling, Inelastic dark matter at the LHC lifetime frontier: ATLAS, CMS, LHCb, CODEX-b, FASER, and MATHUSLA. Phys. Rev. D 99, 015021 (2019). arXiv:1810.01879
M. Cobal et al., Z-boson decays into an invisible dark photon at the LHC, HL-LHC, and future lepton colliders. Phys. Rev. D 102, 035027 (2020). arXiv:2006.15945
M. D’Onofrio, O. Fischer, Z.S. Wang, Searching for dark photons at the LHeC and FCC-he. Phys. Rev. D 101, 015020 (2020). arXiv:1909.02312
P. Fayet, \(U\)-boson production in \(e^+e^-\) annihilations, \(\Psi \) and \(\Upsilon \) decays, and light dark matter. Phys. Rev. D 75, 115017 (2007). arXiv:hep-ph/0702176
R. Essig, P. Schuster, N. Toro, B. Wojtsekhowski, An electron fixed target experiment to search for a new vector boson \(A^{\prime }\) decaying to \(e^+e^-\). JHEP 02, 009 (2011). arXiv:1001.2557
L. Barze et al., Radiative events as a probe of dark forces at GeV-scale \(e^+e^-\) colliders. Eur. Phys. J. C 71, 1680 (2011). arXiv:1007.4984
M. Karliner, M. Low, J.L. Rosner, L.-T. Wang, Radiative return capabilities of a high-energy, high-luminosity \(e^+e^-\) collider. Phys. Rev. D 92, 035010 (2015). arXiv:1503.07209
M. He, X.-G. He, C.-K. Huang, Dark photon search at a circular \(e^+e^-\) collider. Int. J. Mod. Phys. A 32, 1750138 (2017). arXiv:1701.08614
S. Biswas, E. Gabrielli, M. Heikinheimo, B. Mele, Dark-photon searches via ZH production at \(e^+e^-\) colliders. Phys. Rev. D 96, 055012 (2017). arXiv:1703.00402
M. He, X.-G. He, C.-K. Huang, G. Li, Search for a heavy dark photon at future \(e^+e^-\) colliders. JHEP 03, 139 (2018). arXiv:1712.09095
L. Marsicano et al., Dark photon production through positron annihilation in beam-dump experiments. Phys. Rev. D 98, 015031 (2018). arXiv:1802.03794
J. Jiang et al., Production and constraints for a massive dark photon at electron-positron colliders. Chin. Phys. C 44, 023105 (2020). arXiv:1910.07161
J.-J. Blaising, P. Roloff, A. Sailer, U. Schnoor, Physics performance for dark matter searches at \(\sqrt{s} = \) 3 TeV at CLIC using mono-photons and polarised beams. arXiv:2103.06006
J. Kalinowski, W. Kotlarski, P. Sopicki, A.F. Zarnecki, Simulating hard photon production with WHIZARD. Eur. Phys. J. C 80, 634 (2020). arXiv:2004.14486
J. Kalinowski, W. Kotlarski, K. Mekala, P. Sopicki, A.F. Zarnecki, Sensitivity of future \(e^+e^-\) colliders to processes of dark matter production with light mediator exchange. Eur. Phys. J. C 81, 955 (2021). arXiv:2107.11194
J. Kalinowski, W. Kotlarski, K. Mekala, P. Sopicki, A.F. Zarnecki, Dark matter searches with mono-photon signature at future \(e^+e^-\) colliders, Proceedings of the XXVIII International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2021), Stony Brook University, New York, USA, 12-16 April 2021. arXiv:2107.12730
X. Chen, Z. Hu, Y. Wu, K. Yi, Search for dark photon and dark matter signatures around electron–positron colliders. Phys. Lett. B 814, 136076 (2021). arXiv:2001.04382
J.P. Lees et al., (BaBar Collabolaration), Search for a dark photon in \(e^+e^-\) collisions at BaBar. Phys. Rev. Lett. 113, 201801 (2014). arXiv:1406.2980
J.P. Lees et al., (BaBar Collabolaration), Search for invisible decays of a dark photon produced in collisions at BaBar. Phys. Rev. Lett. 119, 131804 (2017). arXiv:1702.03327
B. Ablikim et al. (BESIII Collabolaration), Dark photon search in the mass range between 1.5 and 3.4 GeV/\(c^2\). Phys. Lett. B 774, 252 (2017). arXiv:1705.04265
A. Anastasi et al., (KLOE Collaboration), Limit on the production of a low-mass vector boson in \(e^+e^- \rightarrow U\gamma \), \(U \rightarrow e^+e^-\), with the KLOE experiment. Phys. Lett. B 750, 663 (2015). arXiv:1509.00740
A. Anastasi et al., (KLOE-2 Collaboration), Combined limit on the production of a light gauge boson decaying into \(\mu ^+ \mu ^-\) and \(\pi ^+ \pi ^-\). Phys. Lett. B 784, 336 (2018). arXiv:1807.02691
E. Kou et al. (Belle II collaboration), The Belle II Physics Book, Prog. Theor. Exp. Phys. 2019, 123C01 (2019). arXiv:1808.10567 (Erratum, Prog. Theor. Exp. Phys. 2020, 029201 (2020))
S.S. Chakrabarty, I. Jaeglé, Search for dark photon, axion-like particles, dark scalar, or light dark matter in Compton-like processes. arXiv:1903.06225
M. Smirnov et al., Light dark bosons in the JUNO-TAO neutrino detector. arXiv:2109.04276
Y. Hochberg, B. von Krosigk, E. Kuflig, T.C. Yu, The impact of dark Compton scattering on direct dark matter absorption searches. arXiv:2109.08168
S. Chakraborti et al., Gamma factory searches for extremely weakly-interacting particles. Phys. Rev. D 104, 055023 (2021). arXiv:2105.10289
X. Wong, Y. Huang, Dark photon production via \(\gamma \gamma \rightarrow \gamma A^{\prime }\). Eur. Phys. J. C 81, 442 (2021). arXiv:2103.15079
T. Behnke et al., The International Linear Collider technical design report—volume 1: executive summary. arXiv:1306.6327
P. Bambade et al., The International Linear Collider: a global project. arXiv:1903.01629
H. Braun et al. (CLIC Study Team), CLIC 2008 parameters, CERN-OPEN-2008-021, CLIC-NOTE-764
M.J. Boland et al. (CLIC and CLICdp Collaborations), Updated baseline for a staged Compact Linear Collider, CERN-2016-004. arXiv:1608.07537
The CEPC Study Group, CEPC Conceptual Design Report: Volume 1—accelerator. arXiv:1809.00285
The CEPC Study Group, CEPC Conceptual Design Report: Volume 2—physics & detector. arXiv:1811.10545
N. Arkani-Hammed, N. Weiner, LHC signals for a superunified theory of dark matter. JHEP 12, 104 (2008). arXiv:0810.0714
M. Baumgart et al., Non-abelian dark sectors and their collider signatures. JHEP 04, 014 (2009). arXiv:0901.0283
M. Goodsell, J. Jaeckel, J. Redondo, A. Ringwald, Naturally light hidden photons in large volume string compactifications. JHEP 11, 027 (2009). arXiv:0909.0515
M. Goodsell, A. Ringwald, Light hidden-sector \(U(1)s\) in string compactifications. Fortschr. Phys. 58, 7126 (2010). arXiv:1002.1840
R. Essig, J. Kaplan, P. Schuster, N. Toro, On the origin of light dark matter species. arXiv:1004.0691
M. Cicoli, M. Goodsell, J. Jaeckel, A. Ringwald, Testing string vacua in the lab: from a hidden CMB to dark forces in ux compactifications. JHEP 07, 114 (2011). arXiv:1103.3705
Briefing Book, European Strategy for particle physics preparatory group. arXiv:1910.11775
I.F. Ginzburg, G.L. Kotkin, V.G. Serbo, V.I. Telnov, Colliding \(\gamma e\) and \(\gamma \gamma \) beams based on the single-pass \(e^+e^-\) colliders (of VLEPP type). Nucl. Instrum. Methods 205, 47 (1983)
I.F. Ginzburg, G.L. Kotkin, S.L. Panfil, V.G. Serbo, V.I. Telnov, Colliding \(\gamma e\) and \(\gamma \gamma \) beams based on single-pass \(e^+e^-\) accelerators II. Polarization effects, monochromatization improvement. Nucl. Instrum. Methods 219, 5 (1984)
V.I. Telnov, The photon collider at ILC: status, parameters and technical problems. Acta Phys. Pol. 37, 1049 (2006). arXiv:physics/0604108
R. Aleksan, A. Apyan, Y. Papaphilippou, F. Zimmermann, Scenarios for circular gamma-gamma Higgs factories, in Proceedings of the 6th International Particle Accelerator Conference (PAC2015), 3-8 May, (Richmond, 2015), p. 2156–2159
W. Chou, Circular accelerator-based & recirculating linac-based \(\gamma \gamma \) collider. Talk at the ICFA Mini-Workshop on future gamma-gamma Collider, 23–26, Tsinghua University (Beijing, China, April 2017)
C. Zhang, W. Chou (for the BggC Study Group), A proposed \(\gamma \gamma \) collider in China. Talk at the Photon Beam Workshop, 27–28 November 2017 (Padova, Italy, 2017)
R. Belusevic, Versatile \(e^+e^-/\gamma \gamma /ep\) facilities at a future circular collider. J. Mod. Phys. 8, 1 (2017). arXiv:1805.06360
R. Belusevic, An \(e^+e^-/\gamma \gamma /ep\) accelerator complex at a future circular collider. JHEP 5, 425 (2019)
P.S. Bhupal Dev, R.N. Mohapatra, Y. Zhang, Probing TeV scale origin of neutrino mass at future lepton colliders via neutral and doubly-charged scalars. Phys. Rev. D 98, 075028 (2018). arXiv:1803.11167
Y.-C. Guo, C.-X. Yue, Z.-C. Liu, The signatures of doubly charged leptons in future linear colliders. J. Phys. G Nucl. Part. Phys. 44, 085004 (2017). arXiv:1611.08843
L. Rahili, A. Arhrib, R. Benbrik, Associated production of SM Higgs with a photon in type-II seesaw models at the ILC. Eur. Phys. J. C 79, 940 (2019). arXiv:1909.07793
M. Demirci, A.I. Ahmadov, Neutralino pair production via photon–photon collisions at the ILC. Phys. Rev. D 94, 075025 (2016). arXiv:1610.09398
G.-Li Liu, F. Wang, K. Xie, X.-F. Guo, Probing lepton flavor violation signal via \(\gamma \gamma \rightarrow l_i {\bar{l}}_j\) in the left-right twin Higgs model at the ILC. Phys. Rev. D 96, 035005 (2017). arXiv:1701.00947
H. Yang, Z.-Q. Chen, C.-F. Qiao, NLO QCD corrections to exclusive quarkonium-pair production in photon-photon collision. Eur. Phys. J. C 80, 806 (2020). arXiv:2006.05351
M. Köksal, Model-independent study on the anomalous \(\tau {\bar{\tau }} \gamma \) couplings at the ILC. Nucl. Phys. B 971, 115520 (2021). arXiv:2104.01003
T.G. Rizzo, New physics beyond the Standard Model at \(\gamma \gamma \) colliders. Nucl. Instrum. Methods A 472, 37 (2001). arXiv:hep-ph/0008037
F. Bechtel et al., Studies for a photon collider at the ILC. Nucl. Instrum. Methods A 564, 243 (2006). arXiv:physics/0601204
S.C. İnan, A.V. Kisselev, A search for axion-like particles in light-by-light scattering at the CLIC. JHEP 06, 183 (2020). arXiv:2003.01978
S.C. İnan, A.V. Kisselev, Polarized light-by-light scattering at the CLIC induced by axion-like particles. Chin. Phys. C 45, 043109 (2021). arXiv:2007.01693
S.C. İnan, A.V. Kisselev, Probing anomalous quartic \(\gamma \gamma \gamma \gamma \) couplings in light-by-light collisions at the CLIC. Eur. Phys. J. C 81, 664 (2021). arXiv:2009.09712
S.C. İnan, A.V. Kisselev, Probing anomalous \(\gamma \gamma \gamma Z\) couplings through \(\gamma Z\) production in \(\gamma \gamma \) collisions at the CLIC. JHEP 10, 121 (2021). arXiv:2108.04478
A. Belyaev, N. D. Christensen, A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model. Comput. Phys. Commun. 184, 1729 (2013). arXiv:1207.6082
G. Cowan, K. Cranmer, E. Gross, O. Vitells, Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71, 1554 (2011). arXiv:1007.1727
L. Di Luzio, M. Giannotti, E. Nardi, L. Visinelli, The landscape of QCD axion models. Phys. Rep. 870, 1 (2020). arXiv:2003.01100
V. Berestetskii, E. Lifshitz, V. Pitaevskii, Quantum Electrodunamics: Volume 4 (Course of Theoretical Physics), Second edition (Butterworth-Heinemann, 1982), p. 354–359
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Appendix A
Appendix A
The matrix element of the process (4) is given by the sum of s- and u-channel diagrams presented in Fig. 3. Correspondingly, we get
where
The Mandelstam variable u is equal to
where \(\theta \) is a scattering angle of the DP in the center-of-mass frame of the colliding particles (see Fig. 2). For \(m_{A'}=0\), \(\varepsilon = 1\), the above formulas coincide with well-known formulas for the Compton scattering [121].
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İnan, S.C., Kisselev, A.V. Search for invisible dark photon in \(\gamma e\) scattering at future lepton colliders. Eur. Phys. J. C 82, 592 (2022). https://doi.org/10.1140/epjc/s10052-022-10552-1
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DOI: https://doi.org/10.1140/epjc/s10052-022-10552-1